Make the Dressing: Combine all ingredients in a saucepan and whisk to combine. Bring mixture to a boil over medium heat, then remove from heat and stgrain through a fine-mesh sieve.

In a medium skillet, cook bacon until crisp. Transfer to paper towels to drain.

Pull meat from chickens and cut into bite-size pieces. Place chicken in bowl with the celery, scallions, bacon, and avocados and toss gently. Add three-quarters of the dressing and toss, adding more dressing if the mixture seems dry.

Line a serving platter with lettuce leaves, top with chicken mixture, sprinkle parsley over top and serve.